Randomized Subsystem Descent for Fermion-to-Qubit Mapping

TL;DR

The paper introduces Randomized Subsystem Descent, an efficient algorithm for optimizing fermion-to-qubit mappings by iteratively optimizing subsystems, significantly reducing resource overhead in quantum simulations.

Contribution

It generalizes randomized block coordinate descent to fermion-to-qubit mapping optimization, enabling scalable and efficient reductions in Hamiltonian complexity.

Findings

Achieves significant reduction in Pauli weight across benchmarks.

Handles large models like 16x16 Hubbard and 54-mode molecules.

Demonstrates computational efficiency by focusing on subsystems.

Abstract

We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively samples a tractable subsystem from the full Hamiltonian, performs optimization within the subsystem under a given metric, and then reintegrates the updated subsystem into the global operator. Restricting the optimization to a subsystem at each iteration ensures computational efficiency, bypassing the dimensional bottlenecks that usually hinder global search heuristics. We benchmark our algorithm on one- and two-dimensional lattice hopping models, the Hubbard model with up to $16 \times 16$ sites, alongside a collection of molecular electronic-structure Hamiltonians with up to 54 modes and more than 180,000 Pauli strings. Across all benchmarks, our method consistently provides appreciable reduction in (weighted) Pauli weight, suggesting that Randomized Subsystem Descent is a practical and scalable framework for lowering the resource overhead of finding hardware-efficient Hamiltonian encodings.